I have never understood why Zeno's paradoxes are considered so profound.
Consider what an instant of time is. Is it a non-zero chunk of time smaller than any other finite chunk of time? In this case, we are defining an instant as an infinitesimal chunk of time. If we posit that such a thing exists, then why can't an infinitesimal distance (which the arrow travels in that time) exist?
The other option is to define an instant of time as no time at all. Not the smallest, simply zero. Saying that since you cannot move a non-zero distance in zero time is valid. However, a chunk of time is not composed of an infinite series of zero time chunks, just like 0.00000...1 is not equal to 0 + 0 + 0... There is a gap between zero and infinitesimal that cannot be bridged by zeros alone.
Consider what an instant of time is. Is it a non-zero chunk of time smaller than any other finite chunk of time? In this case, we are defining an instant as an infinitesimal chunk of time. If we posit that such a thing exists, then why can't an infinitesimal distance (which the arrow travels in that time) exist?
The other option is to define an instant of time as no time at all. Not the smallest, simply zero. Saying that since you cannot move a non-zero distance in zero time is valid. However, a chunk of time is not composed of an infinite series of zero time chunks, just like 0.00000...1 is not equal to 0 + 0 + 0... There is a gap between zero and infinitesimal that cannot be bridged by zeros alone.